Results 1 to 10 of about 214 (38)
Symmetric graphs of valency seven and their basic normal quotient graphs
Open Mathematics, 2021 We characterize seven valent symmetric graphs of order 2pqn2p{q}^{n} with ...
Pan Jiangmin, Huang Junjie, Wang Chao
doaj +1 more source
Base sizes of primitive groups of diagonal type
Forum of Mathematics, Sigma, 2023 Let G be a permutation group on a finite set $\Omega $ . The base size of G is the minimal size of a subset of $\Omega $ with trivial pointwise stabiliser in G. In this paper, we extend earlier work of Fawcett by determining the precise base
Hong Yi Huang
doaj +1 more source
Open Mathematics, 2020 A Cayley graph Γ\Gamma on a group G is called a dual Cayley graph on G if the left regular representation of G is a subgroup of the automorphism group of Γ\Gamma (note that the right regular representation of G is always an automorphism group of Γ ...
Pan Jiangmin
doaj +1 more source
The edge-regular complete maps
Open Mathematics, 2020 A map is called edge-regular if it is edge-transitive but not arc-transitive. In this paper, we show that a complete graph Kn{K}_{n} has an orientable edge-regular embedding if and only if n=pd>3n={p}^{d}\gt 3 with p an odd prime such that pd≡3{p}^{d ...
Yu Xue, Lou Ben Gong
doaj +1 more source
Constructing continuum many countable, primitive, unbalanced digraphs [PDF]
, 2009 We construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are ...
David, Josephine Emms, M. Evans
core +2 more sources
Most primitive groups are full automorphism groups of edge-transitive hypergraphs [PDF]
, 2014 We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,Y^G) = G for a random subset Y of X, tends to 1 as n tends to infinity.
Babai, Laszlo, Cameron, Peter J.
core +2 more sources
2-closures of primitive permutation groups of holomorph type
Open Mathematics, 2019 The 2-closure G(2) of a permutation group G on a finite set Ω is the largest subgroup of Sym(Ω) which has the same orbits as G in the induced action on Ω × Ω.
Yu Xue, Pan Jiangmin
doaj +1 more source
Maximal subgroups of finite groups avoiding the elements of a generating set [PDF]
, 2018 We give an elementary proof of the following remark: if G is a finite group and { g1, \u2026 , gd} is a generating set of G of smallest cardinality, then there exists a maximal subgroup M of G such that M 29 { g1, \u2026 , gd} = 05. This result leads us
Lucchini, Andrea, Spiga, Pablo
core +1 more source
A classification of primitive permutation groups with finite stabilizers [PDF]
, 2015 We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.Comment: Accepted in J.
Aschbacher +14 more
core +2 more sources
Point regular groups of automorphisms of generalised quadrangles [PDF]
, 2010 We study the point regular groups of automorphisms of some of the known generalised quadrangles. In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles.
Ascher +23 more
core +2 more sources